In my experience, even when set up correctly, the HD-25 is a very hot running motor. The integral exhaust/intake/carburetor design is prone to overheating the fuel in the carburetor. Once the carburetor/exhaust/intake get too hot, the fuel can and will boil in the carburetor making it impossible to start the motor until it cools down enough to run again. They can, however, be serviceable motors.
Remember that these motors are around 70 years old, and that means that the water pump AND the water tube seal should be replaced. I own a 1947 HD-25 that cooled fine the first time I ran it, then overheated quickly the next time it ran. After giving me fits, it turned out that the water tube seal/grommet had swelled up from exposure to water. The tiny, maybe 3/16" opening, was closed up significantly, choking off the water supply causing overheating.
Back to the original post, there is a gasket between the gearcase and the midsection that separates water from the gear oil. If you separate the two, then you really need to reseal that gasket, or better yet buy or make one. That is a very important gasket.
Here is a picture of the water tube seal/grommet: